They are fortunate in have a more effective tank barrier than Tibet has. Pretty difficult to put a carrier task force between Tibet and China.
Indeed.
...If that condition was met, they would probably put up another obstacle, like requiring an agreement on the PRC's position on Arunachal Pradesh and Aksai Chin.
The disputes over Arunchal Pradesh and Aksai Chin are between the PRC and Indianot Tibet. I'm not sure what China would achieve by seeking to force the Tibetan Government in Exile to acknowledge the validity of a PRC position on these areas.
Tibet
does claim Bhutan and Part of Ladakh (the ancient kingdom of which Aksai Chin was once part) as part of it's cultural sphere but 'ceded' Aksai Chin to the then British Occupied India in 1904 and AP (effectively) in 1914. In all practical senses India has in effect long since abandoned Tibet to its fate.
Tibet is pivotal from a Chinese perspective in terms of Aksai Chin. The tripartite agreement signed in Simla was (in effect) bilateral between Lhasa and Delhi. At the time the Chinese were only concerned with their Eastern border with Tibet.
The status of Tibet is important because for 2000 years the border between India and China was effectively undefined. It's only since 1950 that it became such an issue with the PRC invasion of Tibet. Zhou-en-Lai convinced Nehru that with the British were 'imperialists' and thus that the McMahon line agreement was also 'imperialist'. Nehru apparently didn't understand the Chinese position in respect of the McMahon line. At any rate he evidently failed to grasp the significance enough to raise the issue.
China also didn't bring the issue up again so presumably Nehru concluded the McMahon line
was accepted by China, which of course it wasn't. The 1954 Panchseel agreement avoided the issue of the Aksai Chin border directly and again both parties said nothing.
By 1959 when China 'announced' that it rejected the McMahon line it was too late and China was already effectively 'in occupation'. China presumably maintained its claim to AP in the assumption that by renouncing its claim on AP it would obtain legalisation of it's occupation of Aksai Chin. It was as naive of Nehru as it was sharp of Zhou to remain silent on this.
There is evidence that far from being 'stabbed in the back' over this issue as many Indians believe, Nehru was well aware of Chinese incursions long before the Indian public and that the Chinese were laying the Tibet-Xinjiang road as early as 1955 yet said and did nothing. The motivation for this may have been simply to protect the Panchsheel agreement.
Whatever the reason, Nehru failed to realise or take advantage of the opportunities he had at the time. The 'discovery' of this road was (in hindsight) merely a useful pretext for the 62 war.
It would be fair to say both sides have missed opportunities to resolve this issue over the last 50 years. First, India failed to take advantage of China's weakness while embroiled in Tibet, Korea and faced domestic issues with Chiang. Later, when China made attempts to stabilise its Indian border after it occupied Tibet, India steadfastly prevaricated.
In the 1960s Zhou-en-Lai, made several trips to India in an attempt to resolve border issues. The Chinese were willing to finally (at least in principle and only for the Eastern border) accept the McMahon Line and wanted to 'negotiate' the the western border between Ladakh and Tibet. The Chinese wanted to do this in stages, Nehru wanted it all at once. Ultimately, nothing came of it.
Since then, China's military strength has far outstripped India's leaving the situation decidedly one sided. Today, China clearly has the upper hand.
Arguably, the root of the problem lies primarily with Nehru for his disregard of the Tibetan situation in favour of a focus on Korea. His heirs refusal to allows access to historical records, adds to the confusion over these issues - although many key records do also exist in London. Chinese deceit and intransigence are also key factors.
This is all covered in
"The Fate of Tibet" by Claude Arpi.